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Prove that quadratic equation (bx+c)^2-{(a^2)(x^4)}=0 has at least 2 real roots for all a,b,c belonging to real numbers.
Prove that quadratic equation (bx+c)^2-{(a^2)(x^4)}=0 has at least 2 real roots for all a,b,c belonging to real numbers.

```
3 years ago

```							Let f(x) = (bx+c)^2-{(a^2)(x^4)}f(0) = (b0+c)^2-{(a^2)(0^4)} = c2 now we know f(0) is positive f(-c/b) = (b(-c/b)+c)^2-{(a^2)((-c/b)^4)} = – {(a^2)((-c/b)^4)} So  f(-c/b) is negative. since f is polynomial it is always continous and it changes sogn from + to  – hence by IVT it must have root between -c/b and 0.also degree of f id 4 and nonn real roo occur in pairs hence 1 real root imply another real root
```
3 years ago
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